Plugin to autosave render every minute
I am not sure if this can be done from within blender while it's rendering. It would require rendering the screenshot while rendering the scene. Something like this could easily be done with a shell script outside of blender. 

OSX example: 

while true; 
    do screencapture ~/Desktop/img$(date +"%Y-%m-%d-%H-%M-%S").jpg
    sleep 10
done


This would take a screenshot every 10 seconds, so needs some adjustments.
And then just cancel with 'Ctrl-C'.

If you only want the script to run for a specific period you could do something like:

end=$((SECONDS+360))

while [ $SECONDS -lt $end ]; 
    do screencapture ~/Desktop/img$(date +"%Y-%m-%d-%H-%M-%S").jpg
    sleep 10
done


This will automatically stop taking screenshots in 6 minutes. 

I think Windows looks like this:

:loop
 For /f "tokens=2-4 delims=/ " %%a in ('date /t') do (set mydate=%%c-%%a-%%b)
 For /f "tokens=1-2 delims=/:" %%a in ('time /t') do (set mytime=%%a%%b)
 import -window root screen%mydate%-%mytime%.jpg
 timeout /t 10
 goto loop